At Cable Congress this week in Amsterdam—a gathering of the world’s biggest cable operators—there is one elephant in the room: ties to Big Mobile.

The majority of the revenue generated by Europe’s cable operators is still from television, according to data from trade group Cable Europe. But last year, nearly 50% of the industry’s €21.9 billion ($30.5 billion) in European Union revenue came from telecom services—28% from Internet and 19% from telephony. Telephony is growing at 6.5% a year, more than TV’s 3.9% growth.

In the race to consolidate Europe’s fragmented telecom space, mobile operators from the U.K. to France and beyond are looking to shore up their businesses by seeking fixed-line assets that can offer all-in-one “quad-play” packages. Vodafone Group beat Liberty Global to buy up Kabel Deutschland last year for about $10 billion.

The world’s biggest cable player, Liberty Global, is fighting back by buying up assets such as Virgin Media and, most recently, Ziggo. It now has four million mobile customers.

“The fit between Kabel Deutschland and Vodafone in Germany is perfect,” he said Wednesday. “They have 32 million mobile customers in Germany, we have eight million video customers. They have almost three million broadband customers, we have two million and growing fast.”

But Mike T. Fries, Liberty Global’s chief executive, said the U.S. group doesn’t need a telecom company behind it.

More than that, he said, consumer demand for content across mobile formats, including smartphones, is no threat to cable’s fundamental business.

“A fixed line into the home with multiple tablets, smartphones and laptops connecting to the Internet from one spot is the only way to go for everything,” Mr. Fries said. “The economics of Wi-Fi connectivity in the home with a broadband connection are compelling.”

Mr. Fries said the group is “solid… We don’t feel a lot of heat in any market we’re in.” Still, he said the company faces a “mix” of competition.

“The telecommunications incumbents are increasingly getting active. BT has a very robust business. That has got our attention. KPN in the Netherlands is being relatively aggressive in terms of their marketing.”

“But what brings us comfort is that our networks are extremely resilient. As fast as we need to run, our broadband networks will run,” said Mr. Fries.

Analysts say growth of video-on-demand and digital services, as well as alliances with Web-based services like Netflix, will be key to the future of cable and whether it can drive business in competition with mobile.

“The whole game is to improve the customer experience,” said Caroline Van Weede, managing director of Cable Europe.